Cannon-Thurston Maps for Kleinian Groups

Mahan Mj

doi:10.1017/fmp.2017.2

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arXiv · 1002.0996

Cannon-Thurston Maps for Kleinian Groups

Mahan Mj

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Abstract

We show that Cannon-Thurston maps exist for degenerate free groups without parabolics, i.e. for handlebody groups. Combining these techniques with earlier work proving the existence of Cannon-Thurston maps for surface groups, we show that Cannon-Thurston maps exist for arbitrary finitely generated Kleinian groups without parabolics, proving conjectures of Thurston and McMullen. We also show that point pre-images under Cannon-Thurston maps for degenerate free groups without parabolics correspond to end-points of leaves of an ending lamination in the Masur domain, whenever a point has more than one pre-image. This proves a conjecture of Otal. We also prove a similar result for point pre-images under Cannon-Thurston maps for arbitrary finitely generated Kleinian groups without parabolics.

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BibTeX RIS

Mahan Mj. 2010-02-04. Cannon-Thurston Maps for Kleinian Groups. https://doi.org/10.1017/fmp.2017.2

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